KM.TIlur \Ki; MOTION T< > URKAT UISTAM'KS 



167 



Aj)j)lying this formula, we find that for the condensational wave a, is 18 10', and 

 for the ilistortional 17'' 10'. Measuring these angles from the horizontal instead of 

 the vertical, they become 71' 50' and 72' 50' respectively. 



Assuming that the true wave path is an arc of a circle, it is easy to calculate the 

 depth reached by the wave path. For a condensational wave it is close on 2,800 

 kil< HUH. The value in the case of the distortional wave is practically the same, though 

 slightly higher. 



From this it follows that the disturbances registered in Europe as the first and 

 second phases of earthquakes which originate in Japan, are due to wave motion which, 

 at the origin, has plunged downwards at an angle of about 72 with the horizon, and 

 has penetrated to a depth of about 3,000 kiloms. from the surface, or to about 0'55 

 of the radius as measured from the centre. 



As to approximate indication, the corresponding values for 30 and 60 may be 

 given. 



These results do not pretend to accuracy, but at any rate they indicate the order 

 of magnitude of the true figures, and indirectly point to the cause of the feebleness 

 of the disturliance due to these waves at a distance from the origin. It will l)e seen 

 that the waves which are spread over the whole surface of the earth, outside a circle 

 of 30 radius round the origin, are those contained within a cone of 50 apical angle 

 at the origin, that is to say, about -^th of the total energy of the shock is dis- 

 tributed over ths of the surface of the earth. 



It will not be without interest to form some idea of the elastic constants at the 

 depth i-eached by the waves of Japanese earthquakes on their path to Europe. 

 Taking the velocities of 14 '5 and 8 '8 kiloms. per second, and an assumed density of 

 3 '5, the wave modulus of elasticity is 



in = 5 '86 X 10 12 for the condensational wave, 

 = 2 '16 X 10 12 for the distortional wave. 



Here n is the rigidity, and putting m = k + J" 4 , where k is the bulk modulus, we 



get the result 



k = 4-24 X 10 12 = bulk modulus. 



Comparing these values with those of granite, as given in Professor KNOTT'C 



